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Cubic-quintic solitons in the checkerboard potential
Rodislav Driben1, Boris A Malomed, Arthur Gubeskys
1Laboratoire de Photonique Quantique et Moléculaire, CNRS, Ecole Normale Supérieure de Cachan, UMR 8537, 94235 Cachan, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
Summary
This study explores a 2D model with nonlinearities, revealing robust multi-peak solitons and stable vortex solitons. The research details beam-splitting and soliton multistability within this complex lattice system.
Area of Science:
- Nonlinear Optics
- Condensed Matter Physics
- Mathematical Modeling
Background:
- The Kronig-Penney (KP) lattice is a well-established model in solid-state physics.
- Nonlinear optical phenomena, such as soliton formation, are crucial in wave propagation.
- Previous studies have explored 1D versions of nonlinear lattice models.
Purpose of the Study:
- To introduce and analyze a novel two-dimensional (2D) model combining a checkerboard potential (KP lattice) with cubic and quintic nonlinearities.
- To investigate the beam-splitting mechanism and soliton multistability in this 2D nonlinear lattice.
- To identify and characterize different types of stable and unstable solitons, including multi-peak and vortex solitons.
Main Methods:
- Development of a 2D mathematical model incorporating checkerboard potential and nonlinear terms.
- Numerical simulations to explore beam propagation and soliton dynamics.
- Application of variational approximation (VA) for analyzing single-peak soliton behavior.
Main Results:
- Discovery of robust families of single- and multi-peak solitons (including five- and nine-peak species) in the semi-infinite gap.
- Demonstration of bistability in soliton families, with both branches proving stable.
- Identification of two stable vortex soliton species (four-peak patterns) and unstable compact "crater-shaped" vortices.
Conclusions:
- The 2D nonlinear lattice model supports robust soliton solutions with unique multi-peak and vortex structures.
- Soliton multistability is a key feature, with stable states existing in finite band gaps.
- The study provides insights into wave localization and stability in complex nonlinear optical systems.
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